Systems or processes that are intended to produce a desired result, say a consistently manufactured industrial product, can be described by inter-related variables. Often, the variables are directly correlated with each other, but there are also situations where the variables are consistent with one another without being directly correlated. For example, a steady-state process where the variables that describe the process are supposed to have constant values contains no correlations between pairs of variables when the process is operating correctly. A variable that is determined only by the totality of a number of other variables will not be directly correlated with any single variable. But, a variable that is sensitive to process variations will change when the process changes no matter whether the correlation is bivariate or multivariate. The overall uncertainties with which measurements of variables characterize a system or process arise from the sizes of the correlations between the variables and the process, from the uncertainties introduced by measuring instruments, and from uncertainties in the system or process itself. This invention addresses such overall uncertainties. Hereafter, a multivariate system or process is simply called a “process”, and the overall uncertainties are called “measuring uncertainties”.
This invention seeks to: model measurements of process variables in such a manner that the measuring uncertainties are uncorrelated with the modeling uncertainties; produce models properly dependent upon the combined measuring uncertainties and modeling uncertainties; identify measurements for which uncertainties may be reduced; determine both measuring and modeling uncertainty limits; detect whether a given set of measurements contains one or more faults; and associate measuring uncertainty limits, modeled values, and modeling uncertainty limits with a set of measurements depending upon how many faults are contained therein. The modeling method used to achieve these goals is a vector modeling method which uses a reference set of measurements corresponding to numerous process variations.
Vector modeling techniques which are based on reference data can generally be applied to any process without process-specific application efforts. Neural networks, while based on reference data, are not generally applicable to a process without process-specific application efforts. Furthermore, neural networks produce modeling uncertainties which are directly correlated with measuring uncertainties. This invention does not require process-specific application efforts and produces modeling uncertainties which are uncorrelated with measuring uncertainties, so neural networks are not discussed further.
The most often used classical vector modeling technique employing a reference matrix of numerical vectors determines a model of one element, the output element, of a given reference vector as a linear combination of the remaining elements, the input elements, in the given reference vector. Effective use of this technique requires that the number of reference vectors be substantially larger than the number of elements in each reference vector. The linear combination coefficients are static because they are determined only from the reference matrix. Once determined, they may be used to model the output element of any new vector, containing the same number of numerical elements as the reference vectors, as a linear combination of the input elements in the new vector. This technique produces modeling uncertainties which are correlated with measuring uncertainties.
A less often used classical vector modeling technique employing a reference matrix of numerical vectors can be used to provide a model of any new vector containing the same number of numerical elements as the reference vectors. The model is a linear combination of the reference vectors and for this technique all elements of the vectors may simultaneously be considered as both input and output elements. Effective use of this technique requires that the number of reference vectors be substantially smaller than the number of elements in each reference vector. The linear combination coefficients are dynamic because they are determined not only from the reference matrix but also from the new vector.
In practice, for a specific process, the above techniques are usually applied after carefully specifying or determining exactly those process variables that should be measured to provide the vectors involved, and perhaps after specifying or determining the contribution of each vector element to the optimal conditions that determine the models. It is also quite common to transform the measurements prior to formation of the vectors involved. But, even after inclusion of such refinements in an application, the fact remains that both techniques ultimately reduce to those described above, and both determine their models from classical least-squares conditions. Specifically, the first classical modeling technique described above minimizes the squares of the differences between the reference and modeled output elements summed over reference vectors, whereas the second classical modeling technique minimizes the squares of the differences between the elements of the new vector and the elements of the modeled vector summed over elements.
It is a general characteristic of these classical techniques that their optimal solutions are very sensitive to even a single fault in one of the input elements. While these techniques can be used to detect that a fault has occurred in a system or process, they cannot automatically identify the input elements that are faulted nor can they offer replacement values for faulted elements, replacement values that might be extremely important for controlling a process after a fault has occurred.
The second classical method was altered by minimizing a new function of the new vector and the modeled vector, providing an improved method for analyzing the states of a system or process (see U.S. Pat. No. 4,937,763 Mott). Models yielded by the improved analysis method of the '763 patent are very tolerant of even multiple faults in the input elements. The modeled elements can be used to detect that a fault or faults have occurred in a system or process, to identify the faulted element or elements, and to offer approximate replacement values for faulted elements. But the analysis method of the '763 patent suffers from a major drawback in that the importance of a given element to the modeling process is quite dependent upon the ratio of its measuring uncertainty to its magnitude. One result of this dependence is that all elements that have large measuring uncertainties and magnitudes near zero require special transformations in order to be modeled accurately.
The second classical method was also altered by minimizing another new optimal function of the new vector and the modeled vector and is embodied in “ModelWare™”, a commercially available product of Triant Technologies, Inc., Nanaimo, British Columbia, Canada offering off-line fault detection, fault isolation, and post-fault control for almost any system or process. The ModelWare™ product's modeling technique treats the combination of measuring and modeling uncertainties as dynamic and based on a theoretical formula. The ModelWare™ product's modeling technique can accurately model vector elements of any magnitude, a significant improvement over the technique of the '763 patent.
Another prior art product, “ModelWare/RT™”, also commercially available from Triant Technologies, Inc., facilitates real-time on-line operation in conjunction with large manufacturing processes. The Model-Ware/RT™ product employs the same modeling technique as the afore-mentioned ModelWare™ product, but the treatment of the combination of measuring and modeling uncertainties is based on modeling a reference matrix.
The optimal function utilized by the ModelWare™ and ModelWare/RT™ products is also utilized in an industrial process surveillance method (see U.S. Pat. No. 5,764,509 Gross et al). The '509 patent minimizes this optimal function in combination with a technique for accommodating time differences which may be necessary to take into account in order to create measurements of variables that represent a given state of a system or process, a technique for choosing nearest-neighbors to create a small reference matrix from a large set of reference vectors, and a technique for very early detection of faults.
The modeling technique utilized by the ModelWare™ and ModelWare/RT™ products suffers from the drawback that the importance of a given element to the modeling process is dependent upon the ratio of combined measuring and modeling uncertainties to its range in the reference data matrix. As a result of this dependence, any elements that have small ranges can dominate the modeling process.
The second classical technique, and the improved technique used in the ModelWare™ and ModelWare/RT™ products as usually applied, also produce modeling uncertainties which are directly correlated with measuring uncertainties. However, both these techniques offer slightly modified applications that produce modeling uncertainties that are uncorrelated with measuring uncertainties, but only for one measurement in each application. The result is that there is no balance between the measuring and modeling uncertainties with the measuring uncertainty larger than the modeling uncertainty for some measurements, as is desired, but vice-versa for other measurements.
The classical and improved vector modeling methods described above are typically used for fault detection with the unproved methods additionally used for fault identification and approximate replacement of faulted measurements. While vector modeling methods have been used to filter noise from measurements, Such a purpose has previously been accomplished by determining the parameters of a model with a specific analytic form. This invention uses vector modeling techniques employing reference sets of actual process measurements to specifically determine and reduce measuring uncertainties.